Practical use of mathematical models, that describe complex physical processes, connected with heat and mass transfer (the working process of diesel engine in particular), often runs into considerable difficulties. These difficulties are engendered by the general character of the problem, the large amount of characteristics considered, the complexity of their interdependence and as a sequence the cumbersomeness and inconvenience the mathematical apparatus itself. To overcome these obstacles it is helpful in some cases to introduce some auxiliary parameters, and in other cases - to find a successful functional parametric representation of the characteristics investigated.
Both above mentioned approaches are components of the parameterization method and play a significant role in solving technological problems by means of mathematical modeling.
Use of parameterization is shown by three examples. The first two of them, (that is: parametric representation by means of a differential equation and introduction of a parameter-vector) directly concern the phenomenological model of an atomized liquid spray which lies at the foundation of the calculation investigations of the diesel working process, which have been conducted in CNITA. The third example is connected with plotting a family of one-modal functions used for representation of injection pressure and to search for approximate solution of the central variational problem for “Diesel engine/fuel injection equipment” system. The parametric representation of injection pressure is useful, on the one hand, for modeling and calculation of a diesel fuel spray, and on the other hand, for determination of basic design elements of the fuel injection equipment.